Exploring the properties of benzenoid hydrocarbons through QSPR modeling and domination-based energy parameters

This article aims to explore two emerging areas of graph theory: chemical graph theory and domination theory. We specifically focus on a graph parameter that combines aspects of graph energy and domination, known as the dominating energy of a simple connected graph. This concept refers to the sum of the absolute values of the eigenvalues of the corresponding dominating matrix. Additionally, we discuss several variants of dominating energy, including total dominating energy, connected dominating energy, and a distance-based variant called hop dominating energy. We also introduce the Estrada version and Resolvent version of these dominating energies and examine their predictive capabilities in relation to a set of 12 physico-chemical properties and the π-electron energy of 35 benzenoid hydrocarbons through linear, quadratic, cubic, and multiple linear regression analyses. As a result, we identify the best predictive models, which have applications in various fields, including health science, pharmaceuticals, production, and design engineering. These best predictive models are tested using k-fold cross-validation to assess their stability. Furthermore, a comparative study is conducted to evaluate how the regression models based on domination-based energy parameters perform against models derived from well-known degree-based topological indices, such as the first and second Zagreb indices, the Forgotten index, the Randic index, and the Wiener index. This analysis aims to demonstrate that the domination-based energy parameters are more effective in predicting the physicochemical properties of the selected benzenoid hydrocarbons. Additionally, an external validation is also performed using another set of 5 benzenoid hydrocarbons to ensure the efficacy of the best-fitting models based on domination parameters.